Fig. 1

Algorithm scheme. At each internal node of the guide tree an instance of the algorithm aligns the homology paths of the two sub-alignments present in the children nodes. Each instance of the aligner requires 3 sparse three-dimensional DP matrices for Match, GapX and GapY (shown in the figure). These matrices contain the column by column likelihood of the 3 respective states. The state, among the 3 possible choices, with the highest likelihood is saved in a fourth traceback matrix (not shown). At the end, the final MSA is generated by traversing the traceback matrix backwards following the path that generates the highest likelihood at each step. GapX and GapY states require a marginalization of multiple possible homology paths. Some of these are highlighted in the figure. The existence of a character is illustrated by the coloured strokes on the trees